Options:
OWC makes aftermarkets that are roughly (or were) in line with the prices of used apple drives of the same capacity. These appear to generally work well, though there are definitely issues of their own, firmware updates, and other things you have to do.
Sintech makes a few adapters that will let you use NVMe drives. The adapters are pretty cheap. Mine was about 15 USD and NVMe drives are both fast and about half the price per GB compared to the mac / OWC drives. The problem with these is that hibernation doesn't work right on the mid-2014. You have to disable it otherwise your mac will crash and hard reboot if you ever enter that mode. There have been very technical fixes that involve extracting the 2015 MBP firmware and flashing it with a chip burner attached to a management interface on the MBP logic board. I think the Adata SX8200 is the current recommendation. Sintech also makes several versions of the adapter, so reading through the last 5-10 pages of that other thread might be worth it. I think it was the type C, but I can't recall.
SUPER IMPORTANT: If you go the Sintech/NVMe route, you HAVE to install at least High Sierra on your original hard drive to make sure that you get the firmware update that lets your Mac boot from an NVMe drive. It will never work otherwise.
All of this is in the macrumors thread linked above. But it's 90+ pages, so I thought I'd summarize.
Personal Experience:
I have the Sintech adapter referred to as the "long black adapter". I think that's the same thing as the type c I mention above. It runs the full length of the nvme drive and has a notched area for a screw. The slot for the nvme drive spring loads in such a way that you insert the drive at a roughly 30 degree angle, and then fasten flat with the screw. People complain about flex from overtightening the screw but I don't think it's enough to cause component failure. In spite of that, I only tightened mine enough to be sure the screw wouldn't come loose on it's own.
I have one of the more power hungry drives (Samsung EVO 960) and I'm sure I'd be fine following the 2015 flashing procedure but the cost of failure is so great that it's still not something I really need to spend time on now. With Dropbox disabled I still get about 5-6 hours on the battery and about 6-7% battery drop closed overnight, which is good enough for my purposes. Also, if you dual boot linux or windows, those appear to hibernate just fine as far as I can tell. Performance on the Samsung is about double what the stock 128G Apple ssd was, but I think that's pretty close to what any NVMe drive will get you in the '14 MBP. APFS works. Encryption works too, but I don't know how nice that plays with dual booting.
If you try to use bootcamp to install Windows, at some point you will probably run into issues during the install. There's a fix for it and it's in that other thread, but I can't remember where it was and don't have the patience to go looking for it. Sorry. It involved opening regedit and changing a part of the install state to the next stage, if that helps.
I had issues with getting Arch to play nice with my MBP, but I do not think that any of that was hard drive related.
As far as the operating system goes, hibernation doesn't work right in OSX, but I think I mentioned that already. High Sierra works fine otherwise. Mojave has a weird thing going on where I consistently crash the first time I try to start it, but then it works fine on the reboot, so that's something to be aware of. The only people I've heard complaining much about that are people with EVO drives, so you might be safe if you go a different direction.
I'm trying to think of anything else, but I'm coming up blank. I think that is the most detailed overview of the other thread and what I've gone through that I can think up. I hope it helps.
